The value of the definite integral \( \int_{-1}^{1} x \ln \left(1^{...

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The value of the definite integral \( \int_{-1}^{1} x \ln \left(1^{x}+2^{x}+3^{x}+6^{x}\right) d x \) equals :
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(a) \( \frac{\ln 2+\ln 3}{2} \)
(b) \( \frac{\ln 2+\ln 3}{3} \)
(c) \( \ln 2+\ln 3 \)
(d) \( \frac{\ln 2+\ln 3}{4} \)
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